def ftTest():
w0 = 1.
delta = .1
tVec = np.linspace(-200., 200., 1000, endpoint=False)
wVec = FT.wVecFromTVec(tVec)
f = np.exp(1j * w0 * tVec - delta * np.abs(tVec))
g = -1. / np.sqrt(2. * np.pi) * (1j / (wVec - w0 - 1j * delta) - 1j /
(wVec - w0 + 1j * delta))
wVec, gFT = FT.FT(tVec, f)
fig, ax = plt.subplots(nrows=1, ncols=1)
#ax.plot(wVec, np.real(g), color = 'blue', label="Analytical")
#ax.plot(wVec, np.real(gFT), color = 'red', label="Numerical")
ax.plot(wVec, np.real(gFT) - np.real(g), color='red', label="Diff")
#ax.plot(tVec, np.real(f), color = 'red', label="f(t)")
plt.legend()
plt.show()
failArr = (np.abs(g - gFT) > 0.1)
if (np.any(failArr)):
print(
"Numerical FT is NOT consistent with analytical result!!! ------ CHECK FAILED!!!"
)
return False
else:
print(
"Numerical FT is consistent with analytical result! ------ CHECK PASSED :)"
)
return True
def numGreenVecWLesser(kVec, wVec, eta, damping):
tVec = FT.tVecFromWVec(wVec)
tVecPos = tVec[len(tVec) // 2:]
GFT = gfNumVecTLesser(kVec, tVecPos, eta, damping)
GFZero = np.zeros((len(kVec), len(tVec) // 2), dtype='complex')
GFT = np.concatenate((GFZero, GFT), axis=1)
wVecCheck, GFW = FT.FT(tVec, GFT)
return GFW
def anaGreenVecW(kVec, wVec, eta, damping):
tVec = FT.tVecFromWVec(wVec)
tVecPos = tVec[len(tVec) // 2:]
GFT = anaGreenVecT(kVec, tVecPos, eta, damping)
GFZero = np.zeros((len(kVec), len(tVec) // 2), dtype='complex')
GFT = np.concatenate((GFZero, GFT), axis=1)
wVecCheck, GFW = FT.FT(tVec, GFT)
assert ((np.abs(wVec - wVecCheck) < 1e-10).all)
return GFW
def expectationSinSinW(wVec, eta, damping):
tVec = FT.tVecFromWVec(wVec)
tVecPos = tVec[len(tVec) // 2:]
expSinSinPos = expectationSinSin(tVecPos, eta)
expSinSinPosTurned = expectationSinSinTurned(tVecPos, eta)
expSinSinPos = -expSinSinPos + expSinSinPosTurned
Zeros = np.zeros((len(tVec) // 2), dtype='complex')
#expSinSin = np.concatenate((expSinSinPos, Zeros), axis=0)
expSinSin = np.concatenate((Zeros, expSinSinPos), axis=0)
dampingArr = np.exp(-damping * np.abs(tVec))
expSinSinDamped = expSinSin * dampingArr
wVecCheck, expSinSinW = FT.FT(tVec, expSinSinDamped)
#gsT = - 2. / np.pi * prms.chainLength
#fac = np.sqrt(1 - 2. * eta * eta / (prms.w0) * gsT)
#return eta**2 / fac * (1j / (wVec - fac * prms.w0 + 1j * damping) - 1j / (wVec + fac * prms.w0 + 1j * damping))
return expSinSinW * np.sqrt(2. * np.pi)